The allocative efficiency and conservation potential of
water laws encouraging investments in
on-farm irrigation technology
Ray Huffaker
∗, Norman Whittlesey
Department of Agricultural Economics, Washington State University, Pullman, WA 99164-6210, USA
Abstract
Agricultural water conservation statutes are emerging in the West encouraging private irrigators to improve on-farm irri-gation efficiency as a basinwide conservation measure. We investigate whether private improvements promote the economic efficiency and conservation of water use basinwide under a wide variety of hydroeconomic circumstances. The standard of efficiency is how an irrigation district manager should optimally invest in improving the irrigation efficiencies of individual farms located along a stream while internalizing intrabasin allocative externalities of these investments. The results indicate that the popular Oregon legislative model may be the least effective in conserving water and promoting economically efficient water allocation. © 2000 Elsevier Science B.V. All rights reserved.
Keywords:Basinwide conservation measure; On-farm irrigation technology; Investments
1. Introduction
Farmers have long been shifting to more techni-cally efficient irrigation methods to capture private benefits from increased crop yield and quality, in-creased efficiency in the use of nutrients and chemi-cals, and reduced irrigation labor costs (Hydrosphere Resource Consultants, 1991). On-farm irrigation ef-ficiency is defined as the ratio of the water stored in the crop root zone for consumptive use to the total water diverted for irrigation (Whittlesey et al., 1986). Increased irrigation efficiency allows farmers to apply water more uniformly across fields, thereby enabling crops to sustain or increase their consumptive use of water from smaller diversions. For example,
improv-∗Corresponding author. Tel.:+1-509-335-3048;
fax:+1-509-335-1173.
E-mail address:huffaker@wsu.edu (R. Huffaker).
ing irrigation efficiency from 25 to 80% reduces the diversion needed to meet a prior crop demand for 2 units of consumptive use from 8 to 2.5 units.
Irrigators, policy makers, environmentalists, and journal commentators generally contend that the reduction in diversion due to increased on-farm ir-rigation efficiency (5.5 units in the above example) constitutes water savings that can be used to increase the reliability of water supplies for both instream uses and irrigation (Columbia and Snake River Irrigators Association (CSRIA, 1994); Honhart, 1995; Moon, 1993; Oregon Environmental Council, 1994; Oregon Trout, 1994; Pagel, 1993). Consistent with this con-tention, the federal government and several western states have passed (or are contemplating passing) agri-cultural water conservation laws encouraging farmers to further invest in improved on-farm irrigation tech-nology. For example, Oregon’s equitable division
policy [Or. Rev. Stat. §537.455 (Supp. 1994)],
tions the reduced diversions between the efficiency improving irrigator (to spread over additional acreage) and the public (to apply to instream uses), and thus is recommended to other western states as awin–win
policy (Honhart, 1995). Washington [SB5527 (1997 and 1998 Regular Sessions)] and Colorado (Honhart, 1995) have considered similar policies over multiple legislative sessions. In another example, the federal Yakima River Basin Water Enhancement Project Act [Pub. L. No. 103–434 §1201] provides public financ-ing for improvements in on-farm irrigation efficiency and earmarks the reduction in diversions to increase the reliability of the water supply for both instream flows and irrigation.
We analyze whether increases in on-farm irrigation efficiency can succeed in meeting the water conser-vation objectives of the above statutes/bills for a wide range of western hydrologic circumstances, and the consequences of a failure to do so on the economic ef-ficiency of water allocation in an irrigated river basin. Our analysis proceeds in two stages. We initially for-mulate a continuous version of an interspatial optimal water allocation model and use the necessary condi-tions to qualitatively explain how an irrigation district manager, interested in maximizing the net economic benefits of water allocation across all agricultural users within a river basin, should invest in improving the on-farm irrigation efficiencies of individual farms. Net economic benefits include the farm specific bene-fits of increasing irrigation efficiency and any external costs inflicted on other water rights holders. This qualitative standard of basinwide efficiency represents how private irrigators should invest in improving irri-gation efficiency if their legal rights to water hold them accountable for the external costs of their decisions.
We next solve the optimal water allocation model by reformulating it as a discrete problem whose solu-tion as an empirical nonlinear programming problem facilitates the introduction of important policy and hydrologic restrictions (i.e. statutory instream flow constraints). The optimal solution provides a numer-ical standard of basinwide efficiency against which the simulated operation of a representative agricul-tural water conservation statute is compared for its allocative efficiency and effectiveness in conserving irrigation water. We conclude by recommending how effective and efficient agricultural water conservation policy should be crafted.
2. A qualitative standard of basinwide economic efficiency
Our focus on the basinwide economic efficiency of increasing on-farm irrigation efficiencies requires the formulation of an optimization-based water allo-cation model falling within the gaps left by previous modeling efforts. The only previous economic model determining optimal basinwide investment in improv-ing on-farm irrigation efficiency investigated the case in which diverted water unconsumed by crops is irre-trievably lost to the basin (i.e. irrigation return flows are zero) (Chakravorty et al., 1995). Because irriga-tion return flows constitute a significant porirriga-tion of stream flows in the West (Hydrosphere Resource Con-sultants, 1991), we extend the analysis to a hydrologic system including irrigation return flows. Our model differs from past optimization-based return flow mod-els (Hsu and Griffin, 1992) by focusing on investment in on-farm irrigation efficiency as the mechanism controlling consumptive water use in agriculture.
Following Chakravorty, Hochman and Zilberman (CHZ), we consider a single irrigation district deliv-ering water over a single irrigation season to equally productive farms located along a river of constant depth and within an irrigated basin of constant width measured in miles (m). Let x represent the distance (m) from the origin of basin inflows (x = 0) to the point at which the irrigation district delivers water to a given farm. The amount of water delivered to, and diverted by, the farm at location x is q(x) and the level of consumptive water use by crops is e(x). Each quantity is in acre feet per square mile (AF/m2). On-farm irrigation efficiency atxis defined as
h[I (x)]= e(x)
q(x) (1)
where 0 ≤ h ≤ 1 is assumed to be an increasing and concave function of an investment undertaken to improve it, I(x) ($/m2), i.e. h′(I ) > 0;h′′(I ) < 0,
diverted from the stream and consumed by crops on the farm (i.e. the unconsumed diversion) eventually returns to the stream. A value δ1 = 0 represents an
“open” hydrologic basin where unconsumed diver-sions are irretrievably lost to the basin. Alternatively,
δ1 =1 represents a “closed” hydrologic basin where
unconsumed diversions return to the river as irrigation return flows. Finally, a value 0 < δ1 <1 represents
a range of intermediate cases in which unconsumed diversions are split between irretrievable losses (i.e. evaporative losses) and irrigation return flows. For the purposes of this paper (i.e. deriving a qualitative standard of basinwide efficiency for investing in im-proved irrigation efficiency), we simplify matters by assuming that irrigation return flow reenters the river at the point of initial diversion.
Letz(x) (AF) denote the volume of instream flow at
xfor a fixed irrigation season. Also, letz′(x) (AF/m) represent the spatial rate of change of instream flow atx, which is given by
z′(x)= −q(x)α+δ1q(x){1−h[I (x)]}α−δ2z(x) (2)
Instream flow adjusts at each location x according to the volume of water diverted and applied over the width of the river basin,q(x)α, the portion of the un-consumed diversion that reenters the river as irrigation return flow, δ1q(x){1−h[I(x)]}α, and the portion of
instream flow lost in seepage to an underlying aquifer,
δ2z(x), where 0≤δ2≤1 is the proportional seepage
rate. For example, a 1980 water budget demonstrates that the Eastern Snake Plain Aquifer System was recharged in the amount of 0.4 MAF with seepage from the Snake River (Hydrosphere Resource Con-sultants, 1991, p. 2.6). For simplicity, we assume that aquifer recharge of the river occurs outside the basin.
The irrigation district manager’s assumed objective is to select diversions,q(x), and levels of investment in irrigation efficiency, I(x), to maximize the total net benefits ($) accruing along the river in a single cropping season, i.e.
subject to equation of motion (2) and where X rep-resents the fixed length of the river within the basin. We introduce nonnegativity conditions on q(x) and
I(x) because corner solutions on the controls turn out to be pivotal in analyzing the basinwide economic efficiency of improving on-farm irrigation efficiency.
Following Takayama (Theorem 8.C.1), (Takayama, 1985) the Lagrangian function ($/m) for this problem is
L=[pf(e)−I]α+λ{−qα+δ1q[1−h(I )]α−δ2z}
+µqq+µII (4)
whereλ =λ(x)($/AF) is the marginal value of in-stream flows atx, and µq andµI are multipliers
as-sociated with the non-negativity restrictions onq(x) andI(x). The spatial designation of each variable is dropped for notational brevity, i.e.z=z(x),q =q(x),
I =I (x), ande=e(x).
The necessary conditions for optimization are
L′(q)=pf′(e)h(I )− {1−[1−h(I )]δ1}λ(x)
Assuming that the manager can optimally divert some quantity of water at x, i.e. q(x)∗ > 0, implies that
µq = 0 in Eq. (5a) by complementary slackness
conditions (5d). Then, optimality condition (5a) re-quires that the diversion at each location x be set at the level balancing the marginal value product of diversion,pf′(e)h(I) (i.e. the marginal value product of consumptive water use weighted by the increase in consumptive use due to an incremental increase in diversion), against the marginal value of instream flow, λ(x), weighted by a term accounting for the extent to which unconsumed diversion reenters the river as irrigation return flow. In short, incrementally increasing diversion atxredistributes water applica-tion to that point, which is optimal only when the marginal benefits atxbalance the opportunity costs of any foregone production at other locations measured byλ(x).
When diversions are set optimally along the river,
for the polar hydrologic cases (Eq. (5a)):
λ(x)=pf′(e)h(I ), (δ1=0) (6a)
λ(x)=pf′(e), (δ1=1) (6b)
In the presence of irrigation return flows (δ1 = 1),
optimal water prices are equated with the marginal value product of consumptive water use,pf′(e). Alter-natively, in the absence of return flows (δ1=0), and
when farms are less than 100% efficient in irrigation (h < 1), optimal water prices are equated with the marginal value product of diverted water, pf′(e)h(I), and thus are set lower at all locations than those in the return flow case. Optimal prices are identical in the two polar cases only when on-farm irrigation efficiency is 100% so that there is no unconsumed diverted water available to reenter the river as irrigation return flow. Eq. (5b) dictates that the manager invest in improv-ing irrigation efficiency atx, i.e.I (x)∗>0, when the marginal net benefits of a positive level of investment offset the unitary marginal cost of investment, in which caseµ1=0 by complementary slackness
con-ditions (5d). The marginal net benefits of investment are measured as the weighted difference between the marginal benefits of increased consumptive water use atx,pf′(e), and the foregone marginal value of any resulting decreased irrigation return flows that would have supplied downstream farms, δ1λ(x), where the
weight is given by the marginal increase in consump-tive water use by crops due to an increase in on-farm irrigation efficiency,qh′(I). In short, a positive level of
investment in increasing on-farm irrigation efficiency is optimal at locationxwhen the net economic impact of trading off downstream for upstream benefits is positive at the margin of consumptive water use, and is greater than the unitary investment cost.
The extent to which such a spatial tradeoff is ex-pected to generate positive marginal benefits depends on underlying hydroeconomic circumstances. In the absence of irrigation return flow (δ1 =0), improved
irrigation efficiency does not effect a spatial tradeoff. To see this, substituteδ1=0 into necessary condition
(5b):
pf′(e)qh′(I )−1=0 (7)
The manager is required only to select an investment level equating the marginal agricultural benefits of increasing irrigation efficiency with the site specific
unitary marginal cost of the investment. The absence of return flows removes the linkage between up-stream and downup-stream water use, so that downup-stream opportunity costs are zero. Consequently, an invest-ment in irrigation efficiency that is cost effective at an individual farm promotes basinwide economic effi-ciency because the associated increase in consumptive water use decreases the portion of the diversion that is irretrievably lost to the basin. A diversion creates agricultural benefits at only one location, so the loca-tion should be as efficient in consumptive water use as is cost effective.
Consider next the polar case in which all uncon-sumed diverted water reenters the river as an irrigation return flow (δ=1). Substitutingλfrom Eq. (6b) into necessary condition (5b) yields a positive value for the slack variable µ1 = α > 0. This signifies that
the marginality condition for investing optimally in irrigation efficiency does not hold anywhere along the river, and thus the optimal investment is held con-stant at zero at all locations, i.e.I (x)∗ = 0, by the complementary slackness conditions (5d). The basin-wide optimal solution is for all farms to continue operating with the status quo irrigation technology at efficiencyh(I =0). In sum, the marginal benefits accruing to the efficiency improving farm are exactly offset by the external costs imposed on a downstream farm which has had its water supply cut short due to decreased irrigation return flow. In intermediate cases (0< δ1<1), these external costs gain greater weight
in devaluing the basinwide net benefits of investing in on-farm irrigation efficiency as the fraction of un-consumed diversion reentering the river as irrigation return flow increases (i.e.δ1, increases toward 1).
In the Section 3, we formulate a more hydrolo-gically complex discrete version of the continuous basinwide optimal water allocation model. The solu-tion of the discrete formulasolu-tion as an empirical non-linear programming problem establishes a baseline against which the economic efficiency and conserva-tion potential of a representative agricultural water conservation statute can be illustrated for a range of hydrologic circumstances.
3. Empirical formulation
The discrete formulation of the optimal water allocation model is given by
max
Eq. (8a) is the discrete objective function which is interpreted the same as its continuous counterpart in Eq. (3). All units of measurement remain the same as in the continuous model except forαwhich repre-sents the basin’s constant cross sectional areal width (m2) in the discrete formulation. Eq. (8b) calculates
the instream flow at a given locationxas the flow at adjacent upstream location x−1 plus the net change in flow between the two locations. Flow decreases be-tween the two points due to diversion atx, i.e.q(x)α, and seepage atx−1, i.e.δ2z(x−1). Flow increases by
the portion of unconsumed diversion atx−1 reenter-ing the river atx, i.e.δ1q(x−1){1−h[I(x−1)]}α. The
nonlinear programming solution solves for the opti-mal instream flows satisfying this recursive relation-ship simultaneously (Howitt, 1996). Eq. (8c) imposes an instream flow constraint requiring that stream flow at each location be at least as large as some publicly determined levelzc. Western states generally rely on
such constraints to protect public instream uses such as hydropower generation, recreation, fish and wildlife habitat. Finally, Eq. (8d) fixes basin inflow (i.e. flow atx =0) at an exogenously determined levelz0.
3.1. Policy simulation model
The discrete optimal water allocation model (8a)–(8d) can be modified to simulate the general operation of a representative agricultural water con-servation policy. Our representative policy is drawn from the Oregon agricultural water conservation statute [Or. Rev. Stat. §537.455 (Supp. 1994)], and the federal Yakima River Basin Water Enhance-ment Project Act (Yakima Project Act) [Pub. L. No. 103–434 §1201, 108 Stat. 4526 (1994)]. Both poli-cies encourage individual farmers to increase on-farm irrigation efficiency with the expectation that water will be conserved. Oregon offers efficiency improving irrigators a portion of the conserved water to spread over additional acreage [§537.470(3) (Supp. 1994)]. The Yakima Project Act authorizes the Secretary of the Interior to provide funding assistance to the efficiency improving irrigators [§1203(j)(3)]. Both policies measure water savings in terms of reduced diversions [Or. Rev. Stat. §537.455(1) (Supp., 1994); Yakima Project Act §1205(a)(1)]. Finally, to satisfy their statutory purposes of increasing water for public instream uses, basin irrigators must be restricted from appropriating conserved water to firm up unfulfilled appropriative rights or to expand those rights.
The above shared characteristics constitute the rep-resentative agricultural water conservation policy that we simulate by adding two sets of restrictions to the discrete model specified in Eqs. (8a)-(8d). First, an equality constraint fixes investment in on-farm irriga-tion efficiency at an arbitrary level,If, exceeding the
baseline optimal value at a given diversion pointxf:
I (xf)=If (9)
Second, to protect any conserved water from further appropriation, a set of inequality constraints restricts all farms along the river to appropriate at most baseline levels,qb(x), i.e.
q(x)≤qb(x), forx =1, . . . , X (10)
3.2. Empirical information
on-farm irrigation efficiency,h[I(x)], and that the as-sociated parameters be calculated. Consistent with the restrictions imposed in the last section, f[·] and h[·] are specified as the following quadratic functions:
f[e(x)]=a0+a1e(x)−a2e(x)2 (11a) h[I (x)]=b0+b1I (x)−b2I (x)2 (11b)
where parametersa0,a1,a2,b0,b1, and b2 are
non-negative.
The parameters for production function (11a) are calculated from data representing a Russet Burbank
commercial potato operation in southern Idaho. The 1997 crop budget formulated by the University of Idaho Cooperative Extension System shows that a square mile of land requires a water application of 1382.4 AF to produce 272,000 cwt of potatoes. This translates into a consumptive water use of e(x) = q(x)h =(1382.4)(0.8) =1105.92 AF/m2, given the budget’s irrigation efficiency of 80%. For the pur-poses of this illustration, we presume that: (1) there is no yield when consumptive water use is zero, i.e.
f (0) = a0 = 0; (2) the consumptive water use de-rived from the crop budget generates the maximum yield, i.e.f′(1105.92) = 0; and (3) the yield curve is a symmetric negative quadratic function so that production is zero at twice the maximum yield con-sumptive use level, i.e.f (2211.84)=0. Under these circumstances, Cramer’s Rule can be applied to solve for the two parameters of the production function from the following system:
425=a1(1105.92)−a2(1223059.05)2,
0=a1(2211.84)−a2(4892236.19)2 (12)
The parameters are calculated to bea1=491.898 and a2=0.222393.
The parameters for the irrigation efficiency invest-ment function (11b) are estimated from data reported in a study linking irrigation application systems of various efficiencies to their total annualized costs in dollars per acre (Roberts et al., 1986, Table 3.2). The OLS estimated irrigation efficiency function is
h(I )=0.5947+0.0000047I −0.000000000023I2
(13) We calculate the seepage rate parameter δ2 (in units
of m−1) from information available in a recent study
of the Eastern Snake River Basin in southern Idaho (Hydrosphere Resource Consultants, 1991, p. 2–4). The Snake River stretches approximately 300 miles across the basin and has an average flow of 4.3 mil-lion acre feet (MAF) in the upper reaches, and 2 MAF in the lower reaches, giving an overall average of 3.15 MAF. Of this 3.15 MAF, approximately 0.4 MAF were lost as seepage to the Eastern Snake Plain Aquifer as reported in a 1980 water budget (Hydro-sphere Resource Consultants, 1991, Table 2–1). Thus, the fractional seepage loss is 0.127 (=0.4–3.15), or
δ2=0.0004 (=0.127–300) per mile of river.
4. Comparison of the basinwide optimal policy with the representative conservation policy
4.1. Presence of irrigation return flow
Fig. 1 compares the operation of the basinwide op-timal water allocation policy with the representative agricultural water conservation policy in the presence of irrigation return flow (δ1=1). Without loss of
gen-erality, we work with the following scaled down hypo-thetical river basin. The basin’s cross sectional areal width is one square mile (i.e. 640 acres or asection
of land), and there are 10 diversion points within the basin. The volume of basin inflow isz0=10,000 AF
in a given irrigation season. The seniority of water rights runs upstream so that, for example, the farm at
x =1 has the most senior right and that at x =10 the least senior right. The instream flow constraint protecting environmental uses is assumed to require that stream flow at each location be at least zc =
1000 AF. Recall that x = 0 represents the location of basin inflow and that diversions do not commence untilx=1.
Consistent with the standard of basinwide efficiency derived in the last section, the optimal policy is to not invest in improved on-farm irrigation efficiency at any diversion point except for that at the bottom of the basin,x =10. The rationale for the investment at
Fig. 1. Comparison of basinwide optimal water allocation policy with the representative agricultural water conservation policy in the presence of return flow: (a) irrigation efficiency under the optimal policy; (b) irrigation efficiency under the representative policy; (c) instream flows under the optimal policy (lower curve) and the representative policy (upper curve); (d) diversion (upper curve), consumptive use (middle curve), and return flow (lower curve) under the optimal policy; (e) diversion (upper curve), consumptive use (middle curve), and return flow (lower curve) under the representative policy.
xf = 5, which increases its irrigation efficiency to
80% (Fig. 1(b)).
Fig. 1(c) plots instream flow under the optimal and conservation policies at each diversion point in the basin. The plots are coincident except atx =5, where instream flow increases by 375 AF under the
conser-vation policy. Fig. 1(d) and (e) shed some light on the hydrologic significance of this augmented flow atx =
square mile cross sectional width of the basin for the basinwide optimal policy (Fig. 1(d)) and the represen-tative water conservation policy (Fig. 1(e)).
Under the optimal policy, farms at interior diver-sion points (0< x < 10) each divert approximately 1473 AF, and given identical irrigation efficiencies of 60%, consume approximately 876 AF (Fig. 1(d), top curve). Diversion and consumptive use decreases a little as one moves downriver due to the impact of seepage losses to the aquifer. The basin inflow
z0=10,000 AF is sufficiently large that the instream flow constraint zc = 1000 AF is nonbinding at all diversion points within the basin except for the last atx=10. The farm at this point has the least senior water right, and thus meets the instream flow con-straint by diverting less water than upstream farms (i.e. 1091.98 AF). However, the optimal policy allows this farm to achieve the same consumptive water use as upstream farms by calling for an investment in on-farm irrigation efficiency which increases it to 72%.
Consistent with the design of the representative conservation policy, each farm is restricted to di-verting at most the basinwide optimal levels. Fig. 1(e) shows that: (1) diversions (upper curve) remain at basinwide optimal levels at all points except for
x = 5 where demanded diversion is reduced by 375 AF (=1473–1098) in response to the increased irrigation efficiency at that point; (2) consumptive water use (middle curve) remains constant at baseline optimal levels at all points; and thus (3) unconsumed diverted water (lower curve) decreases atx = 5 by 375 AF (=597–222), which represents a reduction in the irrigation return flow fromx=5 that replenishes instream flow at downstream reentry pointx =6. In sum, the incremental increase in instream flow due to decreased diversion at the point of increased irri-gation efficiency is exactly offset by the decrease in instream flow due to decreased irrigation return flow at the downstream reentry point.
Consequently, when an irrigator increases irrigation efficiency in the presence of irrigation return flow, the reduction in demanded diversion signals the intrabasin redistribution of water between instream flow and irri-gation return flow rather than the creation of additional water. Reduced diversion gives the illusion of water conservation because instream flow increases between the point at which on-farm irrigation efficiency
in-creases and the point at which unconsumed diversion reenters the river. Conservation policy encouraging irrigators to invest in increased on-farm irrigation ef-ficiency is economically inefficient because illusory water savings cannot generate the additional basin-wide economic benefits needed to offset the cost of investment.
Such policy may become increasingly economi-cally inefficient when it permits the efficiency im-proving farm to mistakenly claim reduced diversion as conserved water to be spread over additional irrigated acreage (e.g. as per Oregon’s equitable division policy discussed in the introduction). The efficiency improving farm’s use of illusory water savings to irrigate additional acreage means that, in reality, water is being taken from other farms in the basin. Such redistribution of water might enhance basinwide economic efficiency if the water were redistributed away from less productive farms, but existing statutory water conservation policies con-tain no restrictions that would generate this result consistently.
4.2. Absence of irrigation return flow
Fig. 2 compares the operation of the basinwide op-timal water allocation policy with the representative agricultural water conservation policy in the absence of irrigation return flows (δ1=0). Recall that, in the
absence of return flows, an investment in improving ir-rigation efficiency that is cost effective at an individual farm also promotes basinwide economic efficiency. Similarly, the conservation potential of the represen-tative agricultural water conservation policy turns out to also depend on whether investment is cost effective. Cost effectiveness depends, in turn, on the availabi-lity of water relative to the level of consumptive use needed to maximize crop yield. We illustrate these results by comparing the optimal with the representa-tive policy during “normal” and “low” flow irrigation seasons.
Fig. 2. Comparison of basinwide optimal water allocation policy with the representative agricultural water conservation in the absence of return flow (normal flow year): (a) irrigation efficiency under the optimal policy; (b) irrigation efficiency under the representative policy; (c) instream flows under the optimal policy (lower curve) and the representative policy (upper curve); (d) diversion (upper curve) and consumptive use (lower curve) under the optimal policy; (e) diversion (upper curve) and consumptive use (lower curve) under the representative policy.
1000 AF. A level of basin inflow meeting these condi-tions for this illustration is z0 =20,000 AF, and this
value underlies Fig. 2(a)–(e).
The basinwide optimal policy is to maintain on-farm irrigation efficiency at the status quo level of 60% (Fig. 2(a)). The reason is that, at the status quo irrigation efficiency, the optimal diversion (≈1859.53
By design, the representative conservation policy increases irrigation efficiency to 80% at x = 5 and holds it at basinwide optimal levels everywhere else (Fig. 2(b)). Also by design, each farm is re-stricted to diverting at most basinwide optimal levels. Fig. 2(e) shows that diversions (upper curve) remain at basinwide optimal levels for all points except for x = 5 where diversion decreases by 472.33 AF (=1859.53–1387.20). Despite the reduced diversion, increasing irrigation efficiency to 80% maintains consumptive water use (lower curve) at the yield maximizing level (i.e. 1105.92 AF in Fig. 2(e)). In-stream flow increases at x =5 by the 472.33 AF of reduced diversion (=11142.14–10669.81, Fig. 2(c)), and this increment is sustained at all downstream di-version points because, in the absence of return flow, the associated decline in unconsumed diversion is irretrievably lost and thus has no offsetting impact on instream flow.
In summary, when unconsumed diversion does not return to the river, and when investment in im-proved irrigation efficiency is cost ineffective because consumptive water use is near the yield maximizing level for the status quo irrigation efficiency, then the representative water conservation policy truly creates additional water in the basin equal to the reduction in demanded diversion at the point of increased irriga-tion efficiency.
Finally, consider the impact of a “low” flow irriga-tion season in which basin inflow is insufficient for each farm to divert enough water to meet the yield maximizing consumptive water use level at the status quo irrigation efficiency of 60% while satisfying the public instream flow constraintzc=1000 AF. A basin
inflow meeting these conditions for this illustration is
z0=10,000 AF, and this value underlies Fig. 3(a)–(e).
The basinwide optimal program roughly divides the difference between basin inflow and the instream flow constraint, i.e. z0−zc =10000−1000 =9000 AF,
equally among the identically productive 10 farms in the basin, so that each farm receives approximately 898 AF to divert while satisfying the instream flow constraint (Fig. 3(d), top curve). Upstream farms re-ceive a bit more water than average, and downstream farms a bit less, due to the accumulation of seep-age losses from the river. The averseep-age diversion of 898 AF would translate into an average consumptive water use of 538.8 AF per farm if each remained
at the status quo irrigation efficiency of 60%, i.e.
(898)(0.6)=538.8. However, this level of consump-tive use is well below the yield maximizing yield, 1105.92 AF. Hence, the optimal policy calls for each farm to increase consumptive use to approximately 668 AF (Fig. 3(d), lower curve) by increasing irriga-tion efficiency to about 74% (Fig. 3(a)).
As before, the representative conservation policy in-creases on-farm irrigation efficiency at x = 5–80% while holding efficiency at all other points constant (Fig. 3(b)). Also as before, diversions are restricted to be no greater than basinwide optimal levels. In contrast to the “normal” flow case, the demanded diversion un-der the conservation policy is not adjusted downward at the efficiency improving farm (x=5), but, similar to the other farms in the basin, remains at the optimal baseline level (Fig. 3(d) and (e), top curves). By divert-ing at the maximum allowable level, the efficiency im-proving farm increases consumptive use to 715.71 AF (Fig. 3(e), bottom curve), and thus makes the great-est possible stride toward the yield maximizing level. However, also in contrast to the “normal” flow case, instream flow is not increased under the conservation policy (i.e. the instream flow curves for the optimal and representative policies are coincident in Fig. 3(c)), and thus water is not conserved. In summary, when uncon-sumed diversion does not return to the river, and when investment in improved irrigation efficiency is cost ef-fective because consumptive water use is far below the yield maximizing level for the status quo irrigation efficiency, then the representative water conservation policy fails to create additional water in the basin.
The overall performance of the representative agri-cultural water conservation policy in the absence of return flow is troublesome because it may be ineffec-tual in conserving water when conservation is needed the most (i.e. during low flow years), and effec-tual when conservation is less important (i.e. during normal flow years).
5. Discussion
Fig. 3. Comparison of basinwide optimal water allocation policy with the representative agricultural water conservation policy in the absence of return flow (low flow year): (a) irrigation efficiency under the optimal policy; (b) irrigation efficiency under the representative policy; (c) instream flows under the optimal policy (lower curve) and the representative policy (upper curve); (d) diversion (upper curve) and consumptive use (lower curve) under the optimal policy; (e) diversion (upper curve) and consumptive use (lower curve) under the representative policy.
private investment in improving on-farm irrigation efficiency, but somehow facilitate bargaining between the efficiency-improving irrigator and negatively impacted water users downstream to voluntarily in-ternalize return flow externalities. Unfortunately, the potentially large transaction costs associated with such bargaining are a major reason that water markets have
Following this logic, another policy option is to encourage only those private investments in on-farm irrigation efficiency that do not decrease the return flows relied upon by downstream appropriators and instream uses. Return flows are not reduced if in-vestment leads to reductions in the water consumed or irretrievably lost to the basin, or if the reduction in irretrievable water loss is at least as large as the increase in consumptive use. Such policy neutralizes the return flow externality, and does not discourage private investments in the absence of irrigation return flows when it leads to net water savings in satisfaction of the above requirements.
The California agricultural water conservation statute is an example of such a policy designed to operate effectively and efficiently under either the presence or absence of irrigation return flow. It grants efficiency improving irrigators a portion of conserved water measured as
the reduction of the amount of water consumed or irretrievably lost in the process of satisfying beneficial uses which can be achieved either by im-proving the technology of the method for diverting, transporting, applying, reusing, salvaging, or recov-ering water, or by implementing other conservation methods.
[Cal. Water Code §10521(a) (West Supp. 1992), boldface added].
Since this definition is consistent with the way in which water is truly conserved in both non-return-flow and return-flow systems, the California statute en-courages private investments in on-farm irrigation efficiency only when such investments lead to actual, and not illusory, water savings. This ensures that such investments enlarge the basinwide economic bene-fits of water use, and not simply redistribute them inefficiently among irrigators along the river.
Although the California agricultural water con-servation statute appears better suited to the gen-eral hydrologic conditions of the West, the Oregon statute measuring conservation in terms of diver-sionary quantities seems to be preferred by other western states designing their own programs (see, e.g. State of Washington House Bill 1113 (1997 Regular Session)), and water-policy commentators (see, e.g. Honhart, 1995; Rawson, 1994). The legislative history of the Oregon statute sheds some light on possible reasons.
Interestingly, Oregon’s current statute amended an earlier version that, identical to California, measured conserved water as “. . .the reduction of the amount of water consumed or irretrievably lost. . .” (Or. Rev. Stat. §537.455 (1)(1987)). However, some agricul-tural interests in the state viewed this definition as overly restrictive, and argued that a more liberal def-inition in terms of reduced diversions would join the equitable-division policy in providing adequate incentives for voluntary water conservation (Moon, 1993). Environmental groups supported the revised statute, apparently under the mistaken perception that reduced diversion could be equated generally with reduced use [see, e.g. Oregon Environmental Coun-cil, 1994; Trout Unlimited of Oregon, 1994; Oregon Trout, 1994]. The state Water Resources Commission agreed that “. . .the concept of ‘irretrievably lost’ often leaves little water defined as ‘conserved’ even though the reduced diversion may be large” (Pagel, 1993). Evidently, Oregon shifted to a less restrictive, but generally inappropriate, standard of water con-servation in a misguided attempt to provide stronger private incentives for voluntary water conservation and increase the quantity of water savings.
they recognized that “. . .reduction of. . .irrigation re-turn flow may indicate a higher farm efficiency but may at the same time produce negligible net savings and adversely impact other owners. . .downstream on the canal or river system” (pp. 6–7). In short, Cali-fornia adopted a relatively restrictive, and generally appropriate, standard of water conservation that is consistent with its emphasis on determining whether a conservation investment will yield true water savings.
6. Concluding comments
The current decade has witnessed the emergence of legislation in the irrigated West encouraging pri-vate investment in on-farm irrigation efficiency to promote agricultural water conservation. The bulk of this legislation focuses on the impact that a farm’s increased irrigation efficiency has on the level of its irrigation diversions and ignores the impact on other components of the hydrologic system. It measures agricultural water conservation as the reduction in a farm’s diversions before and after the increase in ir-rigation efficiency. The focus on irir-rigation diversions may not present a problem when water users along the river are not linked by irrigation return flows. Under these circumstances, reduced diversions truly represent water conservation and improved on-farm irrigation efficiency promotes basinwide economic ef-ficiency since the water allocations of all water users can be increased with the water savings.
However, focusing on a farm’s diversions creates problems when irrigation return flows are an impor-tant component of hydrologic systems, as in many areas of the West. The reduction in diversions no longer measures water conservation. Such a measure conceals the true impact of increasing an individual farm’s irrigation efficiency in a return-flow system, which is to increase the consumptive water use of the efficiency improving farm without creating any new water, and to reduce irrigation return flows supplying water to downstream users. In effect, the efficiency improving farm’s additional consumptive use is funded by an involuntary water transfer and tradeoff of agricultural benefits from a downstream irrigator. Agricultural water conservation legislation defining water conservation in terms of diversions in return flows systems will trigger these types of
trade-offs unexpectedly, and thus fail to optimally manage them to ensure basinwide economic efficiency.
We recommend that states avoid these tradeoffs al-together by following California’s lead in approving only those private conservation investments that pro-duce true water savings. True conservation in return flows systems occurs when crops consume less water (e.g. by irrigating fewer acres, growing crops requiring less water, or deficit irrigation), or water is recovered that is otherwise irretrievably lost.
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